Revision as of 00:10, 20 November 2019

Problem 2

Three identical rectangles are put together to form rectangle, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is feet, what is the area in square feet of rectangle?

$[asy] draw((0,0)--(3,0)); draw((0,0)--(0,2)); draw((0,2)--(3,2)); draw((3,2)--(3,0)); dot((0,0)); dot((0,2)); dot((3,0)); dot((3,2)); draw((2,0)--(2,2)); draw((0,1)--(2,1)); label("A",(0,0),S); label("B",(3,0),S); label("C",(3,2),N); label("D",(0,2),N); [/asy]$

$\textbf{(A) }45\qquad\textbf{(B) }75\qquad\textbf{(C) }100\qquad\textbf{(D) }125\qquad\textbf{(E) }150$

Solution 1

We know that the length of the shorter side of the 3 identical rectangles are all 5 so we can use that by seeing that the longer side of the right rectangle is the same as 2 of the shorter sides of the other 2 left rectangles. This means that $2\cdot{5}\ = 10$ which is the longer side of the right rectangle, and because all the rectangles are congruent, we see that each of the rectangles have a longer side of 10 and a shorter side of 5. Now the bigger rectangle has a shorter length of 10(because the shorter side of the bigger rectangle is the bigger side of the shorter rectangle, which is 10) and so the bigger side of the bigger rectangle is the bigger side of the smaller rectangle + the smaller side of the smaller rectangle, which is $10 + 5 = 15$ . Thus, the area is $15\cdot{10}\ = 150$ for choice $\boxed{\textbf{(E)}\ 150}$ ~~Saksham27

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

Difference between revisions of "2019 AMC 8 Problems/Problem 2"

Revision as of 00:10, 20 November 2019

Problem 2

Solution 1

See Also

@@ Line 1: / Line 1: @@
 =Problem 2=
-Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is  feet, what is the area in square feet of rectangle?
+Three identical rectangles are put together to form rectangle, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is  feet, what is the area in square feet of rectangle?
+<asy>
+draw((0,0)--(3,0));
+draw((0,0)--(0,2));
+draw((0,2)--(3,2));
+draw((3,2)--(3,0));
+dot((0,0));
+dot((0,2));
+dot((3,0));
+dot((3,2));
+draw((2,0)--(2,2));
+draw((0,1)--(2,1));
+label("A",(0,0),S);
+label("B",(3,0),S);
+label("C",(3,2),N);
+label("D",(0,2),N);
+</asy>
 <math>\textbf{(A) }45\qquad\textbf{(B) }75\qquad\textbf{(C) }100\qquad\textbf{(D) }125\qquad\textbf{(E) }150</math>
 ==Solution 1==